I had my hands in all different kinds of clay in high school. Clay can be verry different in the makup inclusing the abrasiveness. Be careful on what you are rubbing against your cars paint.
I am a pretty cheap person but there are some areas that I would rather spend a little more money and get a better product.
Check out this link
Zaino Store
I have used carnuba wax for 40 years and was very happy with the results. Then I tried Zaino products- what a difference. The entire experience has been better- application, protection even washing. The dirt does not adhere to the car as easy, a light rain is like a car wash.
I am now sold on this stuff. They sell a clay bar by its self and sell a lubricant as well.
You should get away from using dish soap. It does not have any value for automotive paint other than stripping the wax off.
I spent $80 on my first order of Zaino products, including clay.
I have waxed my runner several times and my wifes FJ once (she wont let me drive it so......). I have enough product left for about another 6 months and I wax about once a month.
I was dedicated to carnuba wax but not any more, this stuff is excellent